Filter Diagonalization Method Research Articles

Pattern synthesis of nonuniform linear antenna array based on FFDM

To optimize the number, spacing and excitation of nonuniform linear array at the same time, a Fourier basis filter diagonalization method (FFDM) is proposed in this paper. By constructing a set of Hamiltonian operator functions that can be decomposed by orthogonal eigenvectors, the synthesis of nonuniform linear arrays is transformed into a generalized eigenvalue decomposition under Fourier basis. The introduction of Fourier basis can improve the computational rate. The least square method (LSM) is used to solve the array element excitation, which improves the matching accuracy. A number of numerical simulations shown that the proposed algorithm can improve the accuracy of the array factor (AF) pattern of many types of practical arrays reconstruction.

Semiclassical Vibrational Spectroscopy of Real Molecular Systems by Means of Cross-Correlation Filter Diagonalization.

We applied the harmonic inversion technique to extract vibrational eigenvalues from the semiclassical initial value representation (SC-IVR) propagator of molecular systems described by explicit potential surfaces. The cross-correlation filter-diagonalization (CCFD) method is used for the inversion problem instead of the Fourier transformation, which allows much shorter propagation time and is thus capable of avoiding numerical divergence issues while getting rid of approximations like the separable one to the pre-exponential factor. We also used the "Divide-and-Conquer" technique to control the total dimensions under consideration, which helps to further enhance the numerical behavior of SC-IVR calculations and the stability of harmonic inversion methods. The technique is tested on small molecules and water trimer to justify its applicability and reliability. Results show that the CCFD method can effectively extract the vibrational eigenvalues from short trajectories and reproduce the original spectra conventionally obtained from long-time ones, with no loss on accuracy while the numerical behavior is much better. This work demonstrates the possibility to apply the combined method of CCFD and SC-IVR to real molecular potential surfaces, which might be a new way to overcome the numerical instabilities caused by the increase of dimensions.

A high resolution Fourier transform ion trap enabled by image current splicing: a theoretical study.

The relatively high work pressure within an ion trap has limited the implementation of the Fourier transform technique for high resolution mass analysis. The main reason is that high buffer gas pressure will cause the rapid decay of ion oscillations. In this study, an image current splicing method based on the filter diagonalization method (FDM) and the Hilbert transform was developed to increase the resolving power of nondestructive mass analysis in a linear ion trap. First, multiple repeated experiments (or ion trajectory simulations) were performed to collect multiple sets of data. Using the FDM, the frequency component distribution was extracted from short image current transients collected from each experiment. The Hilbert transform was then applied to calculate and normalize the decay envelope of each transient. The relative abundance was calculated by counting the envelopes. Finally, image current transients collected from these multiple experiments were spliced and merged into a whole signal with much longer duration and continuous phase. This splicing method could effectively increase the duration of the image current, and thus improve the mass resolution of the ion trap mass analyzer. The mass resolution (m/Δm) was improved from 183.5 to 5.8 × 103, and the average relative difference was 2.8%. The proposed method resolved 3 adjacent peaks which originally could not be resolved from the raw signal by the fast Fourier transform (FFT). Besides simulated data, this method was also applied to the experimental data collected from a Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer. The influence of electronic noise on the proposed method was also discussed in this study.

Energy-filtered random-phase states as microcanonical thermal pure quantum states

We propose a method to calculate finite-temperature properties of a quantum many-body system for a microcanonical ensemble by introducing a pure quantum state named here an energy-filtered random-phase state, which is also a potentially promising application of near-term quantum computers. In our formalism, a microcanonical ensemble is specified by two parameters, i.e., the energy of the system and its associated energy window. Accordingly, the density of states is expressed as a sum of Gaussians centered at the target energy with its spread corresponding to the width of the energy window. We then show that the thermodynamic quantities such as entropy and temperature are calculated by evaluating the trace of the time-evolution operator and the trace of the time-evolution operator multiplied by the Hamiltonian of the system. We also describe how these traces can be evaluated using random diagonal-unitary circuits appropriate to quantum computation. The pure quantum state representing our microcanonical ensemble is related to a state of the form introduced by Wall and Neuhauser for the filter diagonalization method [M. R. Wall and D. Neuhauser, J. Chem. Phys. 102, 8011 (1995)], and therefore we refer to it as an energy-filtered random-phase state. The energy-filtered random-phase state is essentially a Fourier transform of a time-evolved state whose initial state is prepared as a random-phase state, and the cut-off time in the time-integral for the Fourier transform sets the inverse of the width of the energy window. The proposed method is demonstrated numerically by calculating thermodynamic quantities for the one-dimensional spin-1/2 Heisenberg model on small clusters up to 28 qubits, showing that the method is most efficient for the target energy around which the dense distribution of energy eigenstates is found.

Body-of-revolution finite-difference time-domain modeling of hybrid-plasmonic ring resonators.

Development of a computational technique for the analysis of quasi-normal modes in hybrid-plasmonic resonators is the main goal of this research. Because of the significant computational costs of this analysis, one has to take various symmetries of these resonators into account. In this research, we consider cylindrical symmetry of hybrid-plasmonic ring resonators and implement a body-of-revolution finite-difference time-domain (BOR-FDTD) technique to analyze these resonators. We extend the BOR-FDTD method by proposing two different sets of auxiliary fields to implement multi-term Drude-Lorentz and multi-term Lorentz models in BOR-FDTD. Moreover, we utilize the filter-diagonalization method to accurately compute the complex resonant frequencies of the resonators. This approach improves numerical accuracy and computational time compared to the Fourier transform method used in previous BOR-FDTD methods. Our numerical analysis is verified by a 2D axisymmetric solver in COMSOL Multiphysics.

Surface-emitting photonic crystal terahertz quantum cascade laser adopting uniform triangular prism photonic crystal with a double-metal waveguide

Herein, we investigate surface-emitting photonic crystal terahertz quantum cascade lasers adopting double metal waveguide for high light extraction efficiency by utilizing finite-difference time-domain and filter diagonalization method. For the ease of fabrication and scalability of beam power, only a typical uniform 2D unit cell with triangular lattice and connected metal electrodes are considered in this study. Cylinder or uniform triangular prism photonic crystals are adopted as resonators within the selected unit cell structure. Candidate -point modes for efficient surface-normal emission are searched based on the unit cell analysis as a first step. After that, far-field, field distribution, and light-extraction efficiency are calculated to verify the candidate modes’ suitability by deploying 15(16) × 15 unit cells. Extracted results show that the surface-emitting quantum cascade lasers with triangular prism photonic crystal slabs have the possibility to attain high light-extraction efficiency with Gaussian beam shape even with compact chip size and high active region occupancy.

Reliable e-nose for air toxicity monitoring by filter diagonalization method

This paper introduces a compact, affordable electronic nose (e-nose) device devoted to detect the presence of toxic compounds that could affect human health, such as carbon monoxide, combustible gas, hydrogen, methane, and smoke, among others. Such artificial olfaction device consists of an array of six metal oxide semiconductor (MOS) sensors and a computer-based information system for signal acquisition, processing, and visualization. This study further proposes the use of the filter diagonalization method (FDM) to extract the spectral contents of the signals obtained from the sensors. Preliminary results show that the prototype is functional and that the FDM approach is suitable for a later classification stage. Example deployment scenarios of the proposed e-nose include indoor facilities (buildings and warehouses), compromised air quality places (mines and sanitary landfills), public transportation, mobile robots, and wireless sensor networks.

Efficient calculation of X-ray absorption spectra using Chebyshev-Slepian filter diagonalisation.

The efficient, yet accurate, simulation of X-ray absorption spectra represents a significant challenge for ab initio electronic structure methods. Conventional approaches involve the explicit calculation of all core-excited states spanning the energy range of interest, even though only a small number of these states will contribute appreciably to the spectrum. We here report a different approach, based on a time-independent Chebyshev filter diagonalization scheme, which allows for the X-ray absorption spectrum to be computed without the explicit calculation of the core-excited eigenstates. Furthermore, in a subsequent postprocessing calculation, selected peaks may be analyzed via the calculation of natural transition orbitals, if desired. The scheme presented here is based on a refinement of the time-independent Chebyshev filter diagonalization approach. Previous formulations of this method have been characterized by a requirement for significant "user input" via the (sometimes unintuitive) tuning of various numerical parameters. To circumvent this, we introduce a new class of filters based on discrete prolate spheroidal sequences. We demonstrate that the resulting method, which we term Chebyshev-Slepian filter diagonalization, makes filter diagonalization essentially a black-box procedure. The Chebyshev-Slepian filter diagonalization method is implemented at the second-order algebraic diagrammatic construction level of theory and validated through the calculation of the X-ray absorption spectra of trifluoroacetonitrile and 1,4-benzoquinone.

Nonadiabatic Effect in Photodissociation Dynamics of Thiophenol via the 1ππ* State.

Nonadiabatic photodissociation dynamics of thiophenol (PhSH) and deuterated thiophenol (PhSD) via the 1ππ* state was investigated by a reduced three-dimensional (3D) quantum model based on the associated 3D diabatic potential energy surfaces constructed at the explicitly correlated multireference configuration interaction (MRCI-F12) level with the cc-pVTZ-F12 basis. The lifetimes of the low-lying vibronic S1 states for PhSH and PhSD were calculated using a low-storage filter diagonalization method and were in reasonably good agreement with the available experimental results. The nonadiabatic effect was further examined in the photodissociation process by comparing the results in diabatic and adiabatic models. It was found that the adiabatic lifetimes were about 2-4 times shorter than the exact ones in the diabatic model for both PhSH and PhSD. More importantly, the exact ground wave function including the geometric phase (GP) possessed a node along the C-C-S-H/C-C-S-D torsional coordinate, while the node was absent when GP was not included in the adiabatic model. The node structure of the wave function was a hallmark of GP, which sheds light on the nonadiabatic photodissociation dynamics facilitated by the conical intersections.

A Distributed Edge Computing Architecture to Support Sensing and Detecting Leaks in Waterworks Based on Advanced FDM

High costs of urban services, namely, waterworks, transportation, waste collection, wastewater collection and treatment, energy, and public lighting, require their optimization in management. This optimization can be mostly achieved using dedicated technology and strategy by “building” smart cities and smart grids. This paper illustrates findings related to the application of a designed distributed edge computing system for supervising a network of sensors, located on a special configuration of a pipeline, to detect leaks. The plant to be supervised is a zigzag waterworks with leaks to be simulated by opening and closing taps. The pressure variation is detected by magnetic sensors, which convert pressure variation into electric signal to be processed on-line thanks to an advanced and robust algorithm called a filter diagonalization method that performs a spectral analysis. In this paper, we have also developed a 2-D representation of the leak within the pipeline or waterworks, which is a robust way to see the dimensions or the expansion of the leak in a specific space.

Effect of ion clouds micromotion on measured signal in Fourier transform ion cyclotron resonance: Computer simulation.

Particle-in-cell-based realistic simulation of Fourier transform ion cyclotron resonance experiments could be used to generate ion trajectories and a signal induced on the detection electrodes. It has been shown recently that there is a modulation of "reduced" cyclotron frequencies in ion cyclotron resonance signal caused by Coulomb interaction of ion clouds. In this work it was proposed to use this modulation in order to determine frequency difference between an ion of known m/z and all other ions generating signal in ion cyclotron resonance cell. It is shown that with an increase of number of ions in ion cyclotron resonance trap, the modulation index increases, which lead to a decrease in the accuracy of determination of peak intensities by super Fourier transform resolution methods such as filter diagonalization method.

Correction: Ion collision cross section analyses in quadrupole ion traps using the filter diagonalization method: a theoretical study.

Correction for 'Ion collision cross section analyses in quadrupole ion traps using the filter diagonalization method: a theoretical study' by Ting Jiang et al., Phys. Chem. Chem. Phys., 2016, 18, 12058-12064.

Ion collision cross section analyses in quadrupole ion traps using the filter diagonalization method: a theoretical study.

Previously, we have demonstrated the feasibility of measuring ion collision cross sections (CCSs) within a quadrupole ion trap by performing time-frequency analyses of simulated ion trajectories. In this study, an improved time-frequency analysis method, the filter diagonalization method (FDM), was applied for data analyses. Using the FDM, high resolution could be achieved in both time- and frequency-domains when calculating ion time-frequency curves. Owing to this high-resolution nature, ion-neutral collision induced ion motion frequency shifts were observed, which further cause the intermodulation of ion trajectories and thus accelerate image current attenuation. Therefore, ion trap operation parameters, such as the ion number, high-order field percentage and buffer gas pressure, were optimized for ion CCS measurements. Under optimized conditions, simulation results show that a resolving power from 30 to more than 200 could be achieved for ion CCS measurements.

FUZZY INFERENCE BASED LEAK ESTIMATION IN WATER PIPELINES SYSTEM

Pipeline networks are the most widely used mode for transporting fluids and gases around the world. Leakage in this pipeline causes harmful effects when the flowing fluid/gas is hazardous. Hence the detection of leak becomes essential to avoid/minimize such undesirable effects. This paper presents the leak detection by spectral analysis methods in a laboratory pipeline system. Transient in the pressure signal in the pipeline is created by opening and closing the exit valve. These pressure variations are captured and power spectrum is obtained by using Fast Fourier Transform (FFT) method and Filter Diagonalization Method (FDM). The leaks at various positions are simulated and located using these methods and the results are compared. In order to determine the quantity of leak a 2 × 1 fuzzy inference system is created using the upstream and downstream pressure as input and the leak size as the output. Thus a complete leak detection, localization and quantification are done by using only the pressure variations in the pipeline.

The Filter Diagonalization Method in Antenna Array Optimization for Pattern Synthesis

Pattern synthesis of nonuniform antenna arrays has drawn significant attention because of its wide applications. With the aim of reducing the number of elements in linear and planar arrays, this paper introduces a novel non-iterative method based on the filter diagonalization method (FDM), which was originally applied in the problem of identifying and quantifying chemical molecules with nuclear magnetic resonance (NMR) in quantum mechanical formalism. The proposed method samples the data set from the desired discrete pattern and associates the sample data with a time autocorrelation function of a fictitious dynamical system, which is described by an effective “Hamiltonian” operator that contains the array element information. The “Hamiltonian” operator can be decomposed by a set of orthonormal eigenvectors. Therefore, the original pattern synthesis is converted into solving the general eigenvalue decomposition with Krylov bases. The number of nonuniform array elements depends on the number of the Krylov bases and the sample data. The proposed method can obtain an optimized antenna array to reconstruct the desired radiation pattern with a high accuracy. Numerical examples show that proposed FDM pattern synthesis can use less prior knowledge to achieve the desired pattern with highly sparse antenna arrays.

Efficient Calculations with Multisite Local Orbitals in a Large-Scale DFT Code CONQUEST.

Multisite local orbitals, which are formed from linear combinations of pseudoatomic orbitals from a target atom and its neighbor atoms, have been introduced in the large-scale density functional theory calculation code CONQUEST. Multisite local orbitals correspond to local molecular orbitals so that the number of required local orbitals can be minimal. The multisite support functions are determined by using the localized filter diagonalization (LFD) method [ Phys. Rev. B 2009 , 80 , 205104 ]. Two new methods, the double cutoff method and the smoothing method, are introduced to the LFD method to improve efficiency and stability. The Hamiltonian and overlap matrices with multisite local orbitals are constructed by efficient sparse-matrix multiplications in CONQUEST. The investigation of the calculated energetic and geometrical properties and band structures of bulk Si, Al, and DNA systems demonstrate the accuracy and the computational efficiency of the present method. The representability of both occupied and unoccupied band structures with the present method has been also confirmed.

The filter diagonalization method and its assessment for Fourier transform mass spectrometry

Application of the filter diagonalization method (FDM) to Fourier transform mass spectrometry (FTMS) data is not new. Under certain conditions FDM provides resolution superior to Fourier transform (FT) and was proved to be useful in investigation of space charge phenomena in an ion cyclotron resonance cell (ICR) by O’Connor and Amster research groups. Kozhinov and Tsybin have reported substantial increase in resolution and/or acquisition speed of high-resolution molecular and macromolecular MS data. In light of fundamental difficulty in providing theoretical evaluation of the FDM performance under various spectral and noise conditions, this paper is an empirical investigation aimed at establishing the method's true potentials and areas where it may perform better than currently used technologies. The study was conducted on both synthetic transients and experimental Orbitrap transients. Unlike FT, resolution of FDM depends strongly on noise levels. Consequently, we identify the regimes at which FDM can provide a superior resolution even at moderate signal to noise ratios. Moreover, when individual peaks fail to be resolved either because of the small peak separation or high noise conditions, the FDM solution seems to preserve their cumulative intensity. This preservation of the true intensity seems to be very consistent across rather wide ranges of noise conditions and almost impervious to the peak separation.

Decimated Signal Diagonalization Method for Improved Spectral Leak Detection in Pipelines

Leak detection is an important issue in piping that deals with the management of water resources; nowadays large amounts of water in the network are dispersed as reported in current scientific literature. Among the methods for leak detection in water pipes, spectral analysis is very interesting. A classical spectral method is fast Fourier transform, but in this paper, we present an alternative method of spectral analysis, which has higher performance in terms of resolution and fast processing, namely decimated signal diagonalization (DSD). It is a nonlinear, parametric method for fitting time domain signals represented in terms of exponentially damped time signals. The aim is to reconstruct the unknown components as the harmonic variables, estimating the fundamental complex frequencies, and amplitudes. The DSD method partly uses the principles of the filter diagonalization method (FDM), which constructs matrices of a generalized eigenvalue problem directly from measured time signals of arbitrary length. However, the DSD because of its windowing technique produces a considerable reduction of size of the original data matrix, and consequently acquisition time can be shorter. We have tested the DSD method for leak detection problem in an experimental zigzag pipeline. We show as the DSD method produces good results in terms of resolution than FDM one.

Least-squares fitting of time-domain signals for Fourier transform mass spectrometry.

To advance Fourier transform mass spectrometry (FTMS)-based molecular structure analysis, corresponding development of the FTMS signal processing methods and instrumentation is required. Here, we demonstrate utility of a least-squares fitting (LSF) method for analysis of FTMS time-domain (transient) signals. We evaluate the LSF method in the analysis of single- and multiple-component experimental and simulated ion cyclotron resonance (ICR) and Orbitrap FTMS transient signals. Overall, the LSF method allows one to estimate the analytical limits of the conventional instrumentation and signal processing methods in FTMS. Particularly, LSF provides accurate information on initial phases of sinusoidal components in a given transient. For instance, the phase distribution obtained for a statistical set of experimental transients reveals the effect of the first data-point problem in FT-ICR MS. Additionally, LSF might be useful to improve the implementation of the absorption-mode FT spectral representation for FTMS applications. Finally, LSF can find utility in characterization and development of filter-diagonalization method (FDM) MS.

Multispectrum Approach in Quantitative EEG: Accuracy and Physical Effort

The detection of neurophysiological features by means of electroencephalogram (EEG) is one of the most recurrent medical exams to be performed on human beings. As it stands, EEG trials are not always sufficient to deliver a clear and precise diagnosis for much pathology. Hence, it must be integrated with other exams. However, we can use all additional instrumental exams to improve the quality of the diagnosis because there are other constraints, namely, financial, medical, and individual. This paper presents an original implementation of EEG signal processing using filter diagonalization method to build a bispectrum and contour representation to discover possible abnormalities hidden in the signal for aided-diagnosis. Two different EEG signals are used for this scope. EEG signals are acquired simultaneously with electrocardiograms (ECG) and ergospirometric ones. ECG signals are also processed along with EEGs. A comparison is made with high order spectra approach. All experimental data regarding EEG, ECG, and ergospirometry are acquired during suspected-patient walking along a path of ~32 m for verifying the impact of fatigue on neurophysiological processes and vice versa.